Febrero 18, 2026
10:30
On the Theory of Error-Correcting Codes and Their Role in Cryptography and Quantum Computing
Featured speakers
Dr. Sarah Talbi
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Sara is a lecturer in the Department of Algebra and Number Theory at the University of Sciences and Technology Houari Boumediene (USTHB). She obtained her PhD in algebraic coding theory, where her research focused on the construction of cyclic serial codes, the study of the dimension of hulls of codes over finite chain rings, and double polycyclic codes over rings. She is currently pursuing a second PhD at the Universitat Politècnica de València (UPV), focused on the application of coding theory to the design and analysis of quantum error-correcting codes, as well as on enhancing the security of quantum cryptographic protocols.
The basic problem of coding theory is that of reliable communication over an unreliable channel, where errors inevitably occur during the transmission of information. They are widely used not only in network communication, USB interfaces, and satellite systems but also in data storage devices and other physical media that are inherently prone to errors. Beyond their practical importance, error-correcting codes play a central role in theoretical computer science. As such, coding theory is a subject of interest to both practitioners and theoreticians. The main questions addressed by coding theory are the following:
(i) How to construct codes that can correct a maximal number of errors.
(ii) How to design such codes with efficient encoding and decoding algorithms. In this talk, I focus on the theory of classical error-correcting codes. I will introduce the fundamental concepts of coding theory, including error models, distance, and linear codes, and discuss important families such as Hamming, cyclic, and BCH codes. I will then explore the deep connections between coding theory and cryptography, with particular emphasis on code-based cryptosystems and their relevance to post-quantum security. Finally, I will highlight how classical error-correcting codes provide the mathematical and conceptual foundation for error correction in quantum computing, illustrating their continued importance in the development of quantum technologies.
References
- Huffman, W. C., & Pless, V. (2010). Fundamentals of error-correcting codes. Cambridge University Press.
- Moffat, A. (2019). Huffman coding. ACM Computing Surveys (CSUR), 52(4), 1-35.
- Wang, J., Li, R., Lv, J., & Song, H. (2020). Entanglement-assisted quantum codes fromcyclic codes and negacyclic codes. Quantum Information Processing, 19(5).
- Camps-Moreno, E., L ́opez, H. H., Matthews, G. L., Ruano, D., San–Jos ́e, R., & So- prunov, I. (2024, September). Binary Triorthogonal and CSS-T Codes for Quantum Error Correction. In 2024, 60th Annual Allerton Conference on Communication, Con- trol, and Computing (pp. 01-06). IEEE.
- Ding, C., & Li, C. (2024). BCH cyclic codes. Discrete Mathematics, 347(5), 113918.
- Steane, A. M. (1996). Error correcting codes in quantum theory. Physical Review Letters, 77(5), 793–.
